Turning Bands Method
RMtbm is a univariate or multivaraiate stationary isotropic covariance
model in dimension reduceddim which depends on a univariate or
multivariate stationary
isotropic covariance phi in a bigger dimension fulldim.
For formulas for the covariance function see details.
RMtbm(phi, fulldim, reduceddim, layers, var, scale, Aniso, proj)
The turning bands method stems from the 1:1 correspondence between the isotropic covariance functions of different dimensions. See Gneiting (1999) and Strokorb and Schlather (2014).
The standard case is reduceddim=1 and fulldim=3.
If only one of the arguments is given, then the difference of the two
arguments equals 2.
For d == n + 2, where n=reduceddim and
d==fulldim the original dimension, we have
C(r) = phi(r) + r phi'(r) / n
which for n=1 reduces to the standard TBM operator
C(r) = d/dr [ r phi(r) ]
For d == 2 && n == 1 we have
C(r) = d/dr int_0^r [ r phi(r) ] / [ sqrt{r^2 - u^2} ] d u
‘Turning layers’ is a generalization of the turning bands method, see Schlather (2011).
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Turning bands
Gneiting, T. (1999) On the derivatives of radial positive definite function. J. Math. Anal. Appl, 236, 86-99
Matheron, G. (1973). The intrinsic random functions and their applications. Adv . Appl. Probab., 5, 439-468.
Strokorb, K., Ballani, F., and Schlather, M. (2014) Tail correlation functions of max-stable processes: Construction principles, recovery and diversity of some mixing max-stable processes with identical TCF. Extremes, Submitted.
Turning layers
Schlather, M. (2011) Construction of covariance functions and unconditional simulation of random fields. In Porcu, E., Montero, J.M. and Schlather, M., Space-Time Processes and Challenges Related to Environmental Problems. New York: Springer.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again x <- seq(0, 10, 0.02) model <- RMspheric() plot(model, model.on.the.line=RMtbm(RMspheric()), xlim=c(-1.5, 1.5)) z <- RFsimulate(RPtbm(model), x, x) plot(z)
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